4 Measures Used Variance The average of the mean squared error termsor in other wordsThe difference between the outcome as expected and the mean, then squared, then times the probability and then added up.copyright anbirts

6 Measures Used Is this a useful number?Not to me but we need it to find the:-Standard Deviation which is the square root of the varianceAnd this is a number that can be usedcopyright anbirts

7 Measures Used Following through the current example, with aVariance of 300,000 then theStandard Deviation (sd) is 547.7We may use this to work out the chance of anevent happening. Assuming a normal (bell shaped)distribution then we know that 68.46% of outcomes will be within one sd of the mean, 95.44% within two sds and 99.74% within 3 sdscopyright anbirts

8 Measures usedQuestion. What probability is there that we will make a cash flow of 3,753 or more?1) 3,753 is 247 away from the mean2) 247 represents 247/547.7 = 45.0% of one standard deviation3) Look in the normal probability distribution table4) .45 of an sd = .3264, or area under the curve to the left of this point is 32.64% so area to the right must be 67.365) so there is a 67.36% chance we will make 3,753 or morecopyright anbirts

9 Portfolio TheorySo far we have looked at the risk of one asset on its ownBut normally assets are held as part of a portfolio - two or more assetsWhat happens to our risk measurements when there is more than one asset?Question?What would you do with £5,000,000 andwhy?copyright anbirts

10 Portfolio ConsiderationsWe have two questions about a portfolio1)In a portfolio, what is the expected return of the portfolio?2)In a portfolio of two (or more) assets, will the risk of variability be greater or smaller?We had better find outcopyright anbirts

11 Portfolio Expected ReturnLuckily it is easy to work out as it is simply the weighted average of the returns of the assets in the portfolio.So, two assets A and BExpected Return on A = 5%Expected Return on B = 14%Portfolio made up of ¾ A and ¼ BReturn is .75 (5) (14) = 7.25%copyright anbirts

12 Variance of a PortfolioBut is it that simple for the variance?Clearly notERUmbrellasERERCidercopyright anbirts

13 Variance of a PortfolioThe riskiness of an asset held in a portfolio is different from that of an asset held on its ownVariance can be found using the following formulaVar Rp = w2Var(RA) + 2w(1-w)Cov(RARB)+(1-w)2VarRBCov stands for CovarianceCovariance is a measure of how random variables, A & B move away from their means at the same timecopyright anbirts

14 Variance of a Portfolio continuedWith regard to the formula, we know* The weights (w) and (1-w) of the assets,because we decide what they will be*How to work out the variance of A and Bbecause we have just done it.ButWe just need the covariance and that iseasy to work outcopyright anbirts

15 Variance of A and B and CovarianceWork out variance of each assetA is a Steel companyCol:Prob Return Expected col 2- ER (col4)2 x col 1on steel Returncopyright anbirts

24 Capital Asset Pricing Model CAPMIt was realised that total RISK could be split into two partsDiversifiable or unsystematic risk andUndiversifiable or systematic riskIn additionIt was recognised that if risk could be diversified away cheaply and easily then there should be no reward for taking it onNow look at Table What do you noticecopyright anbirts

25 CAPMHowever even if you had a well diversified portfolio there is a risk, market risk, you could not diversify away because certain risks affect everything e.g. the state of the economy, the price of oil etcHowever these factors do not affect everything to the same degreeTherefore a new measure has to be used which does not measure the total risk of an asset or a portfolio but which measures its risk relative to a well diversified portfoliocopyright anbirts

26 CAPM This measure is called BETABeta = Covariance of Asset and PortfolioVariance of the MarketBeta enables us to estimate the un-diversifiable risk of an asset and compare it with the un-diversifiable risk of a well diversified portfoliocopyright anbirts

27 CAPMExampleFirst we need the covariance between the asset and the marketWe could work it out as we did for the covariance of assets A and BWe may also use the Correlation Coefficient, pa,m, and the SDs of the market and asset as followscopyright anbirts

29 CAPMTo work out what the return should be on any asset all we need do is work out what return we should be getting on a well diversified portfolio, work out the extra risk (beta) involved in the asset under consideration and stick the result into an equationcopyright anbirts

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